There have been special purpose Boolean processors as set forth in U.S. Pat. No. 4,001,789 and general purpose processors can be programmed using logical instructions to evaluate Boolean expressions. These prior art approaches have the drawback of being limited in the case of the special purpose Boolean processors and of being slow and storage inefficient in the case of the general purpose processors. The method of the present invention is performed using a general purpose computer system and is more flexible than prior methods because it enables evaluation of Boolean expressions formed at run time or previously formed Boolean expressions or Boolean expressions which have been modified during a process performed by the computer system. Also in those instances where the number of variables of the Boolean expression is three or greater, which is very common, the present invention is more storage efficient because only three instructions are used by the method to evaluate the Boolean expressions after having first formed and stored two processing control vectors.